I'm finishing up some of my stat HW right now and I have hit a wall. There are two questions that are on the tip of my tongue and I can't answer them! It's maddening!

Anyway, here is the the first question...in question:

Suppose the P(E) = .6 , P(F) = .3, and that E and F are independent events. What is the probability that the student knows the answer to the first question and does NOT know the answer to the second question?

(E=prob of first question and F= prob of second)

I really feel like the solutions are obvious, but nothing is coming to me.

Question two is:

P(E) = .6 and P(F) = .5 and P(E and F) = .4

Given the above, what is the probability that the student knows the answer to EXACTLY one of the questions?

Thanks!

November 6th 2009, 07:12 AM

Grandad

Hello Nohg

Welcome to Math Help Forum!

Quote:

Originally Posted by Nohg

Hello everyone,

I'm finishing up some of my stat HW right now and I have hit a wall. There are two questions that are on the tip of my tongue and I can't answer them! It's maddening!

Anyway, here is the the first question...in question:

Suppose the P(E) = .6 , P(F) = .3, and that E and F are independent events. What is the probability that the student knows the answer to the first question and does NOT know the answer to the second question?

(E=prob of first question and F= prob of second)

I really feel like the solutions are obvious, but nothing is coming to me.

Question two is:

P(E) = .6 and P(F) = .5 and P(E and F) = .4

Given the above, what is the probability that the student knows the answer to EXACTLY one of the questions?

Thanks!

1) If , then (= the probability that the student does not know the answer to the second question) .

And if the events are independent, .

2)

But this is an inclusive OR; in other words, it is the probability that the student knows the answer to question 1 or question 2 or both. So if we want the probability that he knows the answer to exactly one question, we subtract from this the probability that he knows the answer to both. Thus: